Upvote:3
According to most Protestant denominations (plus a few non-Protestant ones) marriage is a God ordained relationship that should model Jesus relationship to the church. It is not primarily for personal pleasure or convenience, it is for holiness. No matter how one gets into it the expectation is that all marriages should be lived out to model more and more each day the way God has commuted himself to the wellbeing of his chosen bride.
The vast majority or Protestants recognize all marriages as binding covenant relationships no matter how they were initiated. There is no particular allowance made for having entered into the relationship as non-believers. Whether the procedure was overseen by a civil magistrate or a church of different beliefs or with no particular proceedings at all, all married couples are treated the same and expected to stay married. A marriage of convenience will be just as binding in the eyes of a Protestant church as any other.
The few exceptions you will find in Protestant circles do not apply to your scenario at all. Civil unions that do not fit the broad scope of Biblical marriage will not be viewed the same way (i.e. same-sex unions, unions between humans and non-humans, polygamous unions, etc. are likely to be rejected by many if not most Protestant churches as not falling under the category of marriage at all).